Atmospheric Electricity - Ultra and Extremely Low Frequency Electromagnetic Fields - page 87

where r p denotes gradient with respect to components of the momentum p .Here
the collision integral S is dependent on the distribution functions of electrons f and
neutral molecules f n . The interested reader is referred to a discussion by Gurevich
and Zybin ( 2001 ) and by Trakhtengerts et al. ( 2002 , 2003 ) for details about solutions
of this equation.
The models of runaway breakdown in the atmosphere are based on the assump-
tion that cosmic rays generate a shower of secondary particles, called an extensive
air shower (EAS), thereby producing seed/secondary relativistic electrons which are
capable of initiating the runaway breakdown in the presence of a strong QE field of
thundercloud (Gurevich et al. 1999 ; Lehtinen et al. 1999 ; Gurevich and Zybin 2001 ,
2004 ; Inan and Lehtinen 2005 ; Roussel-Dupré et al. 2008 ; Milikh and Roussel-
Dupré 2010 ). The incident cosmic ray particle energy to initiate runaway breakdown
was estimated to be greater than or of the order of 10 15 eV (Gurevich et al. 1999 ).
The EAS typically consists of 89 % photons, 10 % electrons with the energy up to
30 MeV and 1 % other particles, largely muons (e.g., Carlson et al. 2008 ).
Modeling of interference between electromagnetic wave radiated by the hori-
zontal branch of the parent lightning discharge and the waves reflected from the
night ionosphere and the ground has shown that the transient electric field in the
mesosphere can exceed the runaway electron threshold that supports the idea of free
electron bunching in the mesosphere by the pulsed electric field (Kudintseva et al.
2010 ).
The numerical simulation has shown that one more conceivable reason for the
existence of runaway is the electron acceleration during the propagation of lightning
streamers and stepped leaders (e.g., Gurevich et al. 2007 ; Carlson et al. 2010 ;
Chanrion and Neubert 2010 ; Celestin and Pasko 2011 ). The secondary fast electrons
with the MeV energies may come out from the radioactive decays of a rest muon
after an IC lightning discharge (Paiva et al. 2009 ).
Despite the threshold E c for conventional breakdown is approximately an order
of magnitude greater than that for runway breakdown, the focusing of the electric
field in the vicinity of any inhomogeneity could lower the value of E c by a factor
of 10 or 30 (Fernsler and Rowland 1996 ) and vice versa, the actual field needs
to be two to three times the runaway threshold E r to get sufficient ionization for
starting of runaways (Rowland 1998 ). It may be suggested that the conventional and
runaway breakdowns develop at different altitudes, which are separated by only a
few kilometers. Once either process is triggered prior to the next one, it can suppress
the other process from triggering because of fast electric field relaxation due to the
air polarization caused by the increase of plasma density. This implies that there
may be a hybrid sprite model in which both the breakdown mechanisms may occur
simultaneously (Roussel-Dupré and Gurevich 1996 ; Yukhimuk et al. 1999 ;Lietal.
2009 , 2010 ; Chanrion and Neubert 2010 ).
An observational hint toward the runaway electron mechanism does occur in
the atmosphere is the observations of the so-called terrestrial gamma ray flashes
(TGFs); that is, short bursts of gamma rays originating from Earth's atmosphere.
These events are believed to be due to Bremsstrahlung emissions from energetic
( 1 MeV) electrons interacting with neutral molecules (e.g., see; Dwyer et al. 2010 ;